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Young, Kar-Keung DavidBiblio.com

Variable Structure Control for Robotics and Aerospace Applications

VON NEUMANN, JOHANN (JOHN). - THE MATHEMATICAL FOUNDATION OF QUANTUM MECHANICSBiblio.com

Mathematische Grundlagen der Quantenmechanik. Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik. Thermodynamik quantenmechanischer Gesamtheiten. 3 Papers.

192847068Berlin Weidmannsche Buchhandlung 1928. 8vo. Full cloth but spine gone. In: "Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen aus dem Jahre 1927". 4469 pp. Von Neumann's papers: pp. 1-57 pp. 245-272 a. pp. 273-291. Internally clean and fine. First printing of von Neumann's importent papers in which he gave a mathematically precise formulation of the foundation of Quantum MeChanics basing the theory on the use of Hilbert spaces."He von Neumann developed between 1927 and 1929 a new mathematical framework of the theory subsequently proved to be the most suitable formalism of nonrelativistic quantum mechanics as we use it today as well as of its extensions the relativistic quantum mechanics of partcles and the quantum theory of fields."Max Jammer "The Conceptual Development og Quantum Mechanics" pp.314-15"Von Neumann’s most famous work in theoretical physics is his axiomatization of quantum mechanics. When he began work in that field in 1927 the methods used by its founders were hard to formulate in precise mathematical terms; "operator" on "functions" were handled without much consideration of their domain or definition to their topological properties: and it was blithely assumed that such "operators" when self-adjoint could always be "diagonalized" as in th finite dimensional case at the expense of introducing "Dirac functions" as "eigenvectors." Von Neumann showed that mathematical rigor could be restored by taking as basic axioms the assumptions that the states of a physical system were poinds of a Hilbert space and that the measurable quantities were Hermitian generally unbounded operators densely efined in that space. This formalism. the practical use of which became available after von Neumann had developed the spectral theory of unbounded Hermitian operators 1929 has survived subsequent developments of quantum mechanics and is still the basisi of non relativistic quantum theory; with the introduction of the theory of distributions it has even become possible to interpret its results in a way similar to Dirac’s original intuition."DSB. hardcover

Herman H. J. Lynge & Søn A/S · Danemark5 500,00 DKK≈ 738,65 €

VAN VLECK, JH - TOWARDS QUANTUM MECHANICS, THE CORRESPONDENCE PRINCIPLE J HBiblio.com

The Absorption of Radiation by multiply periodic Orbits and its relation to the Correspondence Principle and the Rayleigh-Jeans Law. Part I- II. I. Some Extensions of the Correspondence Principle. - II. Calculation of Absorption by multiply period.

192447166Corning N.Y. and Menasha Wisc. The Physical Review 1924. Royal8vo. Full buckram. Gilt lettering to spine. A stamp to top of titlepage and to front free endpaper. In: "The Physical Review. A Journal of Experimental and theoretical Physics" Vol. 24 Second Series. V704 pp. textillustr. Van Vleck's papers: pp. 330-346 a. pp. 347-365. Internally clean and fine. First appearance of Van Vleck's two importent papers in which he clarifies and extends the Principle of Correspondence."Van Vleck made his greatest contribution to the old quantum theory in 1924 when he conceived his correspondence principle for absorption. He demonstrated that in the limit of high quantum numbers there would be a correspondence between absorption by classical multiply periodic systems and by their quantum analogues. His proof depended on interpreting net absorption in the quantum theory as the difference between gross absorption and stimulated emission of radiation an interpretation prompted by a remark of Breit’s. Van Vleck was particularly pleased that his classical theory reproduced the quantum result without the need for stimulated emission which he referred to as "negative absorption." DSB."Van Vleck’s theory of absorption by multiply periodic systems was consistent with the newly derived Kramers theory of dispersion and it convinced Bohr that his correspondence principle applied not only to emission but also to absorption. Further Van Vleck’s 1924 calculation made use of several of the ideas that Werner Heisenberg used in his matrix mechanics a year later. Van Vleck’s work however did not lead in the direction of matrix mechanics. His intent was to explain quantum phenomena especially "negative absorption" in classical terms rather than to devise an internally consistent quantum theory." DSB.In 1977 he shared the Nobel Prize with Philip Anderson and N. F. Mott.Van der Waerden "Sources of Quantum Mechanics" pp. 203 ff. hardcover

Herman H. J. Lynge & Søn A/S · Danemark3 000,00 DKK≈ 402,90 €

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